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MathGroup Archive 2003

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Re: EllipticTheta error message

  • To: mathgroup at
  • Subject: [mg39936] Re: [mg39907] EllipticTheta error message
  • From: Dr Bob <drbob at>
  • Date: Wed, 12 Mar 2003 02:31:22 -0500 (EST)
  • References: <>
  • Reply-to: drbob at
  • Sender: owner-wri-mathgroup at

Version 4.2.1 under WinXP does the same thing.

I think the problem is that the calculation encounters terms like


You need to differentiate WRT the second argument, and Mathematica has 
somehow forgotten that.

EllipticThetaPrime is the derivative with respect to that same second 
argument of EllipticTheta.  Perhaps a fix would be to define the above 
expressions.  For instance,

Derivative[n_][EllipticThetaPrime][a_, b_, c_] := Block[{bb},
  D[EllipticThetaPrime[a, bb, c], {bb, n}] /. bb -> b]
Derivative[k_Integer][Derivative[0, n_Integer, 0][EllipticThetaPrime]][
        a_, b_, c_] := Block[{
      bb}, D[EllipticThetaPrime[a, bb, c], {bb, k + n}] /. bb -> b]

That doesn't eliminate the error message, but together with the following, 
it does:

f[x_] = EllipticTheta[3, x, 1/E^(0.1)]^2/10
Series[f@x, {x, 1, 4}]

Maybe that's the right answer; I don't know.

What we might need is to make Mathematica forget the EllipticThetaPrime 
function.  Something like this:

D[EllipticTheta[a_, b_, c_], b_] =.

But that fails.  I'm not sure what has to be unprotected to make that work.


On Tue, 11 Mar 2003 02:36:43 -0500 (EST), Enrique Zeleny 
<ezeleny at> wrote:

> Version 4.1 on Linux gives a spurious error message
> In[1]:= Series[EllipticTheta[3, x, 1/E^(1/10000000000)]^2/
> 10000000000, {x, 1, 4}]
> EllipticThetaPrime::argr:
> EllipticThetaPrime called with 1 argument; 3 arguments are expected.
> All EllipticThetaPrime in the result have the correct number of arguments
> Enrique Zeleny
> UAP, Mexico

majort at
Bobby R. Treat

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